`BookProof.HarmonicOscillator.memLp_harmonicDifferential` (n : ℕ) : MemLp (fun x : ℝ => -(deriv (deriv (hermiteC n)) x) + ((x ^ 2 / 4 : ℝ) : ℂ) * hermiteC n x) 2 (volume : Measure

Proved

BookProof.HarmonicOscillator.memLp_harmonicDifferential

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHarmonicOscillatorEsa.

BookProof.HarmonicOscillator.memLp_harmonicDifferential (n : ℕ) : MemLp (fun x : ℝ => -(deriv (deriv (hermiteC n)) x) + ((x ^ 2 / 4 : ℝ) : ℂ) * hermiteC n x) 2 (volume : Measure ℝ)

Formalization note: Lean 4 identifier BookProof.HarmonicOscillator.memLp_harmonicDifferential.

Preamble

-- Generated from ChapterHarmonicOscillatorEsa.lean — theorem BookProof.HarmonicOscillator.memLp_harmonicDifferential
import Definitions.Def_ChapterStrichartzHermiteQG
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHarmonicOscillatorEsa
import Definitions.Def_ChapterHermiteFunctions
open BookProof.HermiteCore
open BookProof.HarmonicOscillator



open MeasureTheory Polynomial BookProof.HermiteCore BookProof.HermiteStrichartzQG
open BookProof.FarisLavine

Formal statement

theorem BookProof.HarmonicOscillator.memLp_harmonicDifferential (n : ℕ) :
    MemLp (fun x : ℝ => -(deriv (deriv (hermiteC n)) x) + ((x ^ 2 / 4 : ℝ) : ℂ) * hermiteC n x)
      2 (volume : Measure ℝ) := by sorry

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